论文标题
生成对抗网络的分布近似和统计估计保证
Distribution Approximation and Statistical Estimation Guarantees of Generative Adversarial Networks
论文作者
论文摘要
生成的对抗网络（GAN）在无监督学习方面取得了巨大的成功。尽管具有显着的经验表现，但关于gan的统计特性的理论研究有限。本文提供了gan的近似值和统计保证，以估计Hölder空间中具有密度的数据分布。我们的主要结果表明，如果正确选择了发电机和鉴别器网络架构，则gan是在诸如Wasserstein-1距离之类的强差异指标下对数据分布的一致估计器。此外，当数据分布表现出低维结构时，我们表明gans能够捕获数据中未知的低维结构并享受快速统计收敛，这不受环境维度的诅咒。我们对低维数据的分析基于具有Lipschitz连续性保证的神经网络的通用近似理论，这可能具有独立的兴趣。
Generative Adversarial Networks (GANs) have achieved a great success in unsupervised learning. Despite its remarkable empirical performance, there are limited theoretical studies on the statistical properties of GANs. This paper provides approximation and statistical guarantees of GANs for the estimation of data distributions that have densities in a Hölder space. Our main result shows that, if the generator and discriminator network architectures are properly chosen, GANs are consistent estimators of data distributions under strong discrepancy metrics, such as the Wasserstein-1 distance. Furthermore, when the data distribution exhibits low-dimensional structures, we show that GANs are capable of capturing the unknown low-dimensional structures in data and enjoy a fast statistical convergence, which is free of curse of the ambient dimensionality. Our analysis for low-dimensional data builds upon a universal approximation theory of neural networks with Lipschitz continuity guarantees, which may be of independent interest.
